The attractiveness of insurance saving products is driven by dividend payments to policyholders and participation in profits. These are mainly constrained by regulatory disposals on profit-sharing on the basis of statutory accounts. Moreover, since both prudential (Solvency II) and financial reporting (IFRS 17) regulations require market consistent best estimate measurement of insurance liabilities, cash-flow projection models have to be used in order to derive the underlying financial incomes. In most cases, such models are based on Monte-Carlo techniques, which simulate future accounting profit and losses needed for profit-sharing mechanisms. In this paper, we deal with modelling future impairment losses on equity securities for financial portfolios. As a matter of fact, if impairment losses are determined on an instrument-by-instrument basis, projection models deal with model points of financial instruments (e.g. groups of shares). Since individual depreciation mechanisms are non-linear, projecting is quite a challenge for model designers. Our motivation is to describe the joint distribution of market value and impairment provision of a book of equity securities, with regard to the French accounting rules for depreciation. The derived results can more effectively represent such an asymmetric mechanism by using our results. Formally, an impairment loss is recognized for an equity instrument if there has been a significant and prolonged decline in its market value below the carrying cost (acquisition value). Such constraints are formalized using an assumption about the dynamics of the equity, and lead to a complex option-like pay-off. Using this formulation, we propose analytical formulas for some quantitative measurements related to the impairment losses of a financial equities book. These are derived from a general framework and some tractable examples are illustrated. We also investigate the operational implementation of these formulas and compare theircomputational time to a basic simulation approach.

中文翻译：

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为市场一致的人寿保险负债评估建模净净持有量

保险储蓄产品的吸引力是由支付给保单持有人的股息和参与利润驱动的。这些主要受制于根据法定账户进行的关于利润共享的监管处置。此外，由于审慎（偿付能力标准II）和财务报告（IFRS 17）法规均要求市场一致地对保险负债进行最佳估计，因此必须使用现金流量预测模型来得出基本的财务收入。在大多数情况下，此类模型基于蒙特卡洛技术，该技术模拟了利润共享机制所需的未来会计损益。在本文中，我们处理了金融投资组合中股票证券的未来减值损失建模。实际上，如果减值损失是按逐笔工具确定的，投影模型处理金融工具（例如股票组）的模型点。由于各个折旧机制是非线性的，因此投影对于模型设计人员是一个很大的挑战。我们的动机是针对法国折旧会计准则，描述一本股本证券的市场价值和减值准备的共同分配。通过使用我们的结果，得出的结果可以更有效地表示这种不对称机制。正式而言，如果权益工具的市场价值长期且长期低于账面成本（购置价值），则确认减值损失。使用关于股权动态的假设将这种约束形式化，并导致类似期权的复杂回报。使用这个公式，我们提出了一些与金融股票账簿的减值损失相关的定量度量的分析公式。这些是从通用框架派生的，并举例说明了一些易于处理的示例。我们还研究了这些公式的运算实现，并将它们的计算时间与基本的模拟方法进行了比较。